Interactive dose manipulation using prioritized constraints

ABSTRACT

In a method of interactive manipulation of the dose distribution of a radiation treatment plan, after an initial candidate treatment plan has been obtained, a set of clinical goals are transferred into a set of constraints. Each constraint may be expressed in terms of a threshold value for a respective quality index of the dose distribution. The dose distribution can then be modified interactively by modifying the threshold values for the set of constraints. Re-optimization may be performed based on the modified threshold values. A user may assign relative priorities among the set of constraints. When a certain constraint is modified, a re-optimized treatment plan may not violate those constraints that have priorities that are higher than that of the modified constraint, but may violate those constraints that have priorities that are lower than that of the modified constraint.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of, and claims the benefit andpriority of U.S. application Ser. No. 15/395,521, filed Dec. 30, 2016,entitled “INTERACTIVE DOSE MANIPULATION USING PRIORITIZED CONSTRAINTS,”the entire contents of which are incorporated herein by reference forall purposes.

BACKGROUND

Modern radiation therapy techniques include the use of IntensityModulated Radiotherapy (“IMRT”), typically by means of an externalradiation treatment system, such as a linear accelerator, equipped witha multileaf collimator (“MLC”). Use of multileaf collimators in general,and an IMRT field in particular, allows the radiologist to treat apatient from a given direction of incidence to the target while varyingthe shape and dose of the radiation beam, thereby providing greatlyenhanced ability to deliver radiation to a target within a treatmentvolume while avoiding excess irradiation of nearby healthy tissue.However, the greater freedom that IMRT and other complex radiotherapytechniques, such as volumetric modulated arc therapy (VMAT), where thesystem gantry moves while radiation is delivered, and three-dimensionalconformal radiotherapy (“3D conformal” or “3DCRT”), afford toradiologists has made the task of developing treatment plans moredifficult. As used herein, the term radiotherapy should be broadlyconstrued and is intended to include various techniques used toirradiate a patient, including use of photons (such as high energyx-rays and gamma rays) and particles (such as electron and protonbeams). While modern linear accelerators use MLCs, other methods ofproviding conformal radiation to a target volume are known and arewithin the scope of the present invention.

Several techniques have been developed to create radiation treatmentplans for IMRT or conformal radiation therapy. Generally, thesetechniques are directed to solving the “inverse” problem of determiningthe optimal combination of angles, radiation doses and MLC leafmovements to deliver the desired total radiation dose to the target, orpossibly multiple targets, while minimizing irradiation of healthytissue. This inverse problem is even more complex for developing arctherapy plans where the gantry is in motion while irradiating the targetvolume. Heretofore, radiation oncologists or other medicalprofessionals, such as medical physicists and dosimetrists, have usedalgorithms to develop and optimize a radiation treatment plan.

Optimization is often used in IMRT to achieve a radiation treatment planthat can fulfill a set of clinical goals in terms of a set of qualityindexes. Quality indexes may include statistical quantities of a dosedistribution produced by a radiation treatment plan. For example,quality indexes may include maximum dose Dmax for a planned targetvolume (PTV), minimum dose Dmin for the PTV, mean dose Dmean for anorgan at risk (OAR), percentage of the PTV receiving 100% of theprescribed dose V100% (i.e., dose coverage), and the like. Clinicalgoals may be expressed in terms of a set of threshold values for the setof quality indexes. For example, clinical goals may include the maximumdose Dmax for the PTV should be less than or equal to 105% of theprescribed dose (i.e., Dmax_PTV≤105%), the minimum dose Dmin for the PTVshould be greater than or equal to 95% of the prescribed dose (i.e.,Dmin_PTV≥95%), the mean dose Dmean to the OAR should be less than 20 Gy(i.e., Dmean_OAR≤20 Gy), the percentage of the PTV receiving 100% of theprescribed dose V100% should be greater than 95% (i.e., V100%>95%), andthe like.

While a physician may be able to recognize a good treatment plan whensuch a plan has been obtained through optimization, it is difficult tospecify a unique set of clinical goals prior to optimization. Onepossible approach is to use an initial set of clinical goals as astarting point to generate a reasonable candidate plan, and theninteractively modify the dose distribution generated by the candidateplan to reach an optimal plan. One way of interactively modifying theplan is to directly make changes to the dose distributions, either inthe three-dimensional fluence map or by modifying the dose volumehistogram (DVH) curves, for various target structures and criticalorgans. In this approach, when a final optimal plan is reached, only theresultant dose distribution is recorded, which by itself may not clearlyconvey the physician's intent when she modified the dose distribution toreach the optimal plan. Therefore, it is desirable to have methods ofinteractively manipulating dose distribution in a treatment plan wherethe physician's intent may be preserved.

SUMMARY

According to some embodiments of the present invention, systems,methods, and apparatuses are provided for interactive manipulation ofthe dose distribution of a radiation treatment plan. For example, afteran initial candidate treatment plan has been obtained, a set of clinicalgoals are transferred into a set of constraints. Each constraint may beexpressed in terms of a threshold value for a respective quality indexof the dose distribution. The threshold value may be referred to as a“constraint location” for the respective quality index. The dosedistribution can then be modified interactively by modifying theconstraint locations for the set of constraints. Re-optimization of thetreatment plan may be performed based on the modified constraintlocations. In this manner, the connection between a clinical goal and aconstraint location is maintained. Thus, the physician's final intent isrecorded as the changed constraint locations. In some embodiments, auser may assign relative priorities among the set of constraints.According to an embodiment, when a certain constraint is modified, are-optimized treatment plan may not violate those constraints that havepriorities that are higher than that of the modified constraint, but mayviolate those constraints that have priorities that are lower than thatof the modified constraint. In another embodiment, the user mayinteractively change the relative priorities for one or moreconstraints. In a further embodiment, two or more constraints may sharethe same priority. In such cases, when a certain constraint is modified,a re-optimized treatment plan either can or cannot violate otherconstraints having the same priority.

In other embodiments of the present invention, for cases where two ormore clinical goals share the same priority or it is not clear whichclinical goal is more important than the other, and the two or moreclinical goals cannot be simultaneously met, an optimization algorithmmay be designed to seek a solution that minimizes a “distance” to aregion where all the clinical goals are met. In one embodiment, a usermay specify a first set of threshold values for a set of quality indexescorresponding to the two or more clinical goals, as well as a second setof threshold values for the set of quality indexes. The constraint ofthe second set of threshold values may be easier to satisfy than thefirst set of threshold values. For example, the second set of thresholdvalues may represent clinically acceptable threshold values, and thefirst set of threshold values may represent desired or preferredthreshold values. A corresponding difference may be determined for eachquality index from the first set of threshold values and the second setof threshold values. An optimal treatment plan may be obtained byoptimizing a cost function that includes a plurality of terms (e.g.,quadratic terms), where each term relates to a respective quality index,and the weight of each term relates to the difference for the respectivequality index.

In yet other embodiments of the present invention, a cost function cantake into account both the quality indexes and their derivatives. Theoptimizer can also support clinical goals where the user has specifiedpreferable trade-offs in advance. For example, the user can specifyclinically insignificant changes as well as clinically significantchanges for each quality index. In some implementations, the costfunction can be generated and dynamically altered during optimization sothat any solution achieving clinically significant improvement in onequality index while only deteriorating the other quality index by aninsignificant amount may be accepted. In one embodiment, the optimizermay change the constraint location whenever the cost function gradientin a space spanned by the quality indexes has a much greater componentwith respect to one quality index compared to the other quality index.

Other embodiments are directed to systems and computer readable mediaassociated with methods described herein.

A better understanding of the nature and advantages of embodiments ofthe present invention may be gained with reference to the followingdetailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic perspective view of a radiation treatment system.

FIG. 2 is a schematic side view of a radiation treatment system.

FIG. 3 shows schematically a photon collimation system in a radiationtreatment system.

FIG. 4 shows an exemplary multileaf collimator (MLC) plane.

FIG. 5 shows a block diagram of an external-beam radiation treatmentsystem of FIGS. 1 and 2.

FIG. 6 illustrates an exemplary user interface that may allow a user tointeractively manipulate the dose distribution of a radiation treatmentplan according to an embodiment of the present invention.

FIG. 7 illustrates an exemplary user interface that can allow a user tointeractively manipulate the dose distribution of a radiation treatmentplan by changing the shape of an optimization structure, according to anembodiment of the present invention.

FIG. 8 shows a simplified flowchart illustrating a method forinteractively manipulating dose distribution of a radiation treatmentplan according to an embodiment of the present invention.

FIG. 9 shows a space spanned by two quality indexes Q₁ and Q₂, whichincludes a region where solution can be found and a region where a setof clinical goals with respect to Q₁ and Q₂ can be simultaneouslyfulfilled, according to an embodiment of the present invention.

FIG. 10 shows a space spanned by two quality indexes Q₁ and Q₂,illustrating a method of determining an optimal radiation treatment planaccording to an embodiment of the present invention.

FIG. 11 shows a space spanned by two quality indexes Q₁ and Q₂,illustrating a method of determining an optimal radiation treatment planaccording to another embodiment of the present invention.

FIG. 12 illustrates an exemplary user interface that may be used in amethod of determining an optimal radiation treatment plan according toan embodiment of the present invention.

FIG. 13 shows a simplified flowchart illustrating a method ofdetermining an optimal radiation treatment plan according to anembodiment of the present invention.

FIG. 14 shows a space spanned by two quality indexes Q₁ and Q₂,illustrating a method of determining an optimal radiation treatment planaccording to an embodiment of the present invention.

FIG. 15 shows a space spanned by two quality indexes Q₁ and Q₂,illustrating a method of determining an optimal radiation treatment planaccording to another embodiment of the present invention.

FIG. 16 illustrates an exemplary user interface that may be used in amethod of determining an optimal radiation treatment plan according toan embodiment of the present invention.

FIG. 17 shows a simplified flowchart illustrating a method ofdetermining an optimal radiation treatment plan according to anembodiment of the present invention.

FIG. 18 shows a block diagram of an example computer system usable withsystem and methods according to embodiments of the present invention.

TERMS

“Radiation” refers to any particles (e.g., photons, electrons, protonsetc.) used to treat tissue, e.g., tumors. Examples of radiation includehigh energy x-rays, gamma rays, electron beams, and proton beams. Thedifferent particles can correspond to different types of radiationtreatments. The “treatment volume” refers to the entire volume that willbe subjected to radiation, and is sometimes referred to as the“irradiated volume.” The “target structure”, “target volume”, and“planning target volume” (“PTV”) refer to tissue intended to receive atherapeutic prescribed dose.

A “radiation treatment plan” can include a dose distribution, machineparameters for achieving the dose distribution for a given patient, andinformation about the given patient. A dose distribution providesinformation about the variation in the radiation dose with spatialpositions within a treatment area of the patient. A “dose distribution”can take many forms, e.g., a dose volume histogram (DVH) or a dosematrix. A DVH can summarize three-dimensional (3D) dose distributions ina graphical 2D format, e.g., where the horizontal axis is the dose(e.g., in units of grays—Gy) absorbed by the target structure (e.g., atumor) and the vertical axis is the volume percentage. In a differentialDVH, the height of a bar at a particular dose indicates the volume ofthe target structure receiving the particular dose. In a cumulative DVH,the height of a bar at a particular dose represents the volume of thestructure receiving greater than or equal to that dose. The cumulativeDVH is generally a curve (e.g., when small bin sizes are used), whereasthe differential DVH is generally a disjoint bar graph. A drawback of aDVH is that it offers no spatial information; i.e., a DVH does not showwhere within a structure a dose is received. A dose matrix can providethe dose that each part of the body receives.

DETAILED DESCRIPTION

The present disclosure relates generally to treatment planning forradiation therapy using external-beam radiation treatment systems, andis more particularly directed to interactive dose manipulation usingprioritized constraints. For example, after an initial candidatetreatment plan has been obtained, a set of clinical goals aretransferred into a set of constraints. Each constraint may be expressedin terms of a threshold value for a respective quality index of the dosedistribution. The dose distribution can then be modified interactivelyby modifying the threshold values for the set of constraints.Re-optimization may be performed based on the modified threshold values.Thus, the physician's final intent is recorded as the changed thresholdvalues. In some embodiments, a user may assign relative priorities amongthe set of constraints. According to an embodiment, when a certainconstraint is modified, a re-optimized treatment plan may not violatethose constraints that have priorities that are higher than that of themodified constraint, but may violate those constraints that havepriorities that are lower than that of the modified constraint.

I. Treatment System

In general, radiation therapy consists of the use of ionizing radiationto treat living tissue, usually tumors. There are many different typesof ionizing radiation used in radiation therapy, including high energyx-rays, electron beams, and proton beams. The process of administeringthe radiation to a patient can be somewhat generalized regardless of thetype of radiation used. External beam therapy (EBT), also calledexternal radiation therapy, is a method for delivering a beam or severalbeams of high-energy x-rays to a patient's tumor. Beams are generatedoutside the patient (usually by a linear accelerator) and are targetedat the tumor site.

FIGS. 1 and 2 depict a radiation treatment system of the type that maybe used in connection with the present invention. Referring to FIG. 1, aperspective view of radiation treatment system (in this case a linearaccelerator) is shown. Typically, such a system is capable of generatingeither an electron (particle) beam or an x-ray (photon) beam for use inthe radiotherapy treatment of patients on a treatment couch 35. Otherradiation treatment systems are capable of generating heavy ionparticles such as protons. For purposes of the present discussion, onlyx-ray irradiation will be discussed. However, it will be appreciated bythose skilled in the art that the same principles apply to othersystems.

Stand 10 supports a rotatable gantry 20 with a treatment head 30. Nextto stand 10 there is arranged a control unit (not shown) that includescontrol circuitry for controlling the different modes of operation ofthe accelerator. A high voltage source is provided within the stand orin the gantry, to supply voltage to an electron gun (not shown)positioned on an accelerator guide located in the gantry 20. Electronsare emitted from the electron gun into the guide (not shown) where theyare accelerated. A source supplies RF (microwave) power for thegeneration of an electric field within the waveguide. The electronsemitted from the electron gun are accelerated in the waveguide by theelectric field, and exit the waveguide as a high energy electron beam,typically at megavoltage energies. The electron beam then strikes asuitable metal target, emitting high energy x-rays in the forwarddirection.

Referring now to FIG. 2, a somewhat more detailed side view of aradiation treatment system of the type that may be used in connectionwith the present invention is shown. A patient P is shown lying on thetreatment couch 35. X-rays formed as described above are emitted fromthe target in the treatment head 30 in a divergent beam 104. Typically,a patient plane 116, which is perpendicular to the page in FIG. 2, ispositioned about one meter from the x-ray source or target, and the axisof the gantry 20 is located on the plane 116, such that the distancebetween the target and the isocenter 178 remains constant when thegantry 20 is rotated. The isocenter 178 is at the intersection betweenthe patient plane 116 and the central axis of beam 122. A treatmentvolume to be irradiated is located about the isocenter 178.

FIG. 3 shows schematically a photon collimation system 300 with upperjaws 310 (i.e., the Y1 and Y2 jaws; the Y1 jaw is omitted for clarity),lower jaws 320 (i.e., the X1 and X2 jaws), and a multileaf collimator(MLC) 330. The field dimensions in the plane 340 at the isocenter 178are indicated. The upper jaws 310, the lower jaws 320, and the leaves332 of the MLC 330 comprise an x-ray blocking material, and arepositioned in the head 30 to define the width of the x-ray beam at thepatient plane. Typically, the jaws 310 and 320 are moveable and, whenfully open, define a maximum beam of about 40 cm×40 cm at the patientplane 116. The MLC 330 is positioned at the exit of the head 30, tofurther shape the x-ray beam. Since its introduction in 1990 the MLC hasbecome a standard feature of most radiation treatment systems. CurrentMLCs sold by the assignee of the present invention use up to 120individually controllable leaves, typically thin slices of tungsten,that can be moved into or out of the x-ray beam under the control ofsystem software.

FIG. 4 shows an exemplary MLC plane having a plurality of leaves 332,arranged in opposing pairs, and an aperture 415 created by selected leafmovements. Radiation passes through and is shaped by the aperture 415.Thus, the MLC can be used to collimate the x-rays to provide conformaltreatment of tumors from various angles (“3D conformal”) as well asintensity modulated radiotherapy (“IMRT”), whereby different radiationdoses are delivered to different portions of the treatment area. Thetreatment volume, i.e., the irradiated volume proximate to the isocenter178 in the path of the x-ray beam, is defined by the jaws 310 and 320,the leaf sequence of the MLC 330, and the collimator angle, i.e., theangle at which the MLC 330 sits in the head 30. Some external radiationtreatment systems may include multiple layers of MLCs. The multiplelayers of MLCs may be positioned at different planes and at differentcollimator angles.

FIG. 5 shows a block diagram of an external-beam radiation treatmentsystem 500 of FIGS. 1 and 2. The radiation treatment system 500 includesa beam source 510, a beam aperture 520, a gantry 530, and a couch 540.The beam source 510 is configured to generate a beam of therapeuticradiation. This beam of radiation may include x-rays, particles, and thelike. The beam aperture 520 includes an adjustable multi-leavecollimator (MLC) 522 for spatially filtering the radiation beam. Thecouch 540 is configured to support and position a patient. The couch 540may have six degrees of freedom, namely the translational offsets X, Y,and Z, and the rotation, pitch, and yaw.

The gantry 530 that circles about the couch 540 houses the beam source510 and the beam aperture 520. The beam source 510 is optionallyconfigured to generate imaging radiation as well as therapeuticradiation. The radiation treatment system 500 may further include animage acquisition system 550 that comprises one or more imagingdetectors mounted to the gantry 530.

The radiation treatment system 500 further includes a control circuitry560 for controlling the operation of the beam source 510, the beamaperture 520, the gantry 530, the couch 540, and the image acquisitionsystem 550. The control circuitry 560 may include hardware, software,and memory for controlling the operation of these various components ofthe radiation treatment system 500. The control circuitry 560 cancomprise a fixed-purpose hard-wired platform or can comprise a partiallyor wholly-programmable platform. The control circuitry 560 is configuredto carry out one or more steps, actions, and other functions describedherein. In some embodiments, the control circuitry 560 may include amemory for receiving and storing a radiation treatment plan that definesthe control points of one or more treatment fields. The controlcircuitry 560 may then send control signals to the various components ofthe radiation treatment system 500, such as the beam source 510, thebeam aperture 520, the gantry 530, and the couch 540, to execute theradiation treatment plan. In some embodiments, the control circuitry 560may include an optimization engine 562 configured for determining aradiation treatment plan. In some other embodiments, the controlcircuitry 560 may not include an optimization engine. In those cases, aradiation treatment plan may be determined by an optimization engine ina separate computer system, and the radiation treatment plan is thentransmitted to the control circuitry 560 of the radiation treatmentsystem 500 for execution.

II. Radiation Treatment Planning

Radiation therapy is generally implemented in accordance with aradiation treatment plan that typically takes into account the desireddose of radiation that is prescribed to be delivered to the tumor, aswell as the maximum dose of radiation that can be delivered tosurrounding tissue. Various techniques for developing radiationtreatment plans may be used. Preferably, the computer system used todevelop the radiation treatment plan provides an output that can be usedto control the radiation treatment system, including the control pointsand the MLC leaf movements. Typically, the desired dose prescribed in aradiation treatment plan is delivered over several sessions, calledfractions.

Several techniques have been developed to create radiation treatmentplans for IMRT or conformal radiation therapy. Generally, thesetechniques are directed to solving the “inverse” problem of determiningthe optimal combination of angles, radiation doses and MLC leafmovements to deliver the desired total radiation dose to the targetwhile minimizing irradiation of healthy tissue. This inverse problem iseven more complex for developing arc therapy plans, such as volumetricmodulated arc therapy (VMAT), where the one or more external treatmentcoordinates, such as the isocenter location, gantry angle, couch angles,and couch offsets, are in motion while irradiating the target volume.Heretofore, radiation oncologists or other medical professionals, suchas medical physicists and dosimetrists, have used one of the availablealgorithms to develop and optimize a radiation treatment plan.

Typically, such planning starts with volumetric information about thetarget tumor and about any nearby tissue structures. For example, suchinformation may comprise a map of the planning target volume (“PTV”),such as a prostate tumor, which is prescribed by the physician toreceive a certain therapeutic radiation dose with allowable tolerances.Volumetric information about nearby tissues may include for example,maps of the patient's bladder, spinal cord and rectum, each of which maybe deemed an organ at risk (OAR) that can only receive a much lower,maximum prescribed amount of radiation without risk of damage. Thisvolumetric information along with the prescribed dose limits and similarobjectives set by the medical professionals are the basis forcalculating an optimized dose distribution, also referred to as fluencemap, which in turn is the basis for determining a radiation treatmentplan. The volumetric information may, for example, be reduced to anobjective function or a single figure of merit that accounts for therelative importance of various trade-offs inherent in a radiationtreatment plan, along with constraints that must be met for theradiation treatment plan to be medically acceptable or physicallypossible.

Treatment planning algorithms can account for the capabilities of thespecific radiation treatment system they are used with, for example, theenergy spectrum and intensity profile of the radiation beam, and thecapabilities of the MLC. Generally speaking, treatment planningalgorithms proceed by calculating the radiation dose received by eachvoxel in the treatment volume, adjusting one or more variable systemparameters, such as the angle of irradiation or the positions of the MLCleaves, and then recalculating the dose received by each voxel. Thisprocess is ideally performed iteratively until an optimized plan isreached. However, the amount of time needed to perform the large numberof calculations for each iteration places a practical limit on thenumber of iterations that can be performed. Accordingly, the algorithmis terminated after a predetermined amount of time, after apredetermined number of iterations, or after some other practical limitis reached. Generally speaking, there is a trade-off between theaccuracy and speed of the different algorithms available for treatmentplanning.

III. Interactive Dose Manipulation Using Prioritized Constraints

Optimization is often used in IMRT to achieve a radiation treatment planthat can fulfill a set of clinical goals in terms of a set of qualityindexes. While a physician may be able to recognize a good treatmentplan when such a plan has been obtained through optimization, it mightbe difficult to specify a unique set of clinical goals prior tooptimization. One possible approach may be to construct a cost functionusing an initial set of reference values for a set of quality indexes(the initial set of reference values are usually not the same asclinically acceptable threshold values but may be related to them), andperform optimization using the cost function to generate a reasonablecandidate treatment plan. The candidate treatment plan produces aninitial dose distribution. A user may then interactively modify thecandidate plan by directly make changes to the initial dosedistributions, either in the three-dimensional dose distribution or bymodifying the dose volume histogram (DVH) curves, for various targetstructures and critical organs. In this approach, when a final optimalplan is reached, only the resultant dose distribution is recorded, whichby itself may not clearly convey the physician's intent when shemodified the dose distribution to reach the optimal plan. For example,it may not be clear whether the physician was trying to decrease themean dose to an organ at risk (OAR), or to increase the percentage ofthe target volume (PTV) receiving 100% of the prescribed dose, when shemodified the dose distribution. Thus, it may not be clear how thephysician's intent could be transferred to a different fieldarrangement, a different fractionation scheme, or a modified patientanatomy. Another way of interactively modifying the plan may be tomodify the initial set of clinical goals and then re-optimize the planwith the modified goals. This approach, however, may not allow directstudy of trade-offs between different clinical goals. For example, aphysician may wish to explore how much a quality index related to oneclinical goal can be improved without deteriorating another qualityindex related to another clinical goal by more than a clinicallysignificant amount.

According to an embodiment of the present invention, in a method ofinteractive manipulation of the dose distribution of a radiationtreatment plan, after an initial candidate treatment plan has beenobtained, a set of clinical goals are transferred into a set ofconstraints, which are used for interactive re-optimization. Inmathematical optimization, constraint optimization is the process ofoptimizing an objective function with respect to some variables in thepresence of constraints on those variables. The objective function iseither a cost function or energy function which is to be minimized, or areward function or utility function, which is to be maximized.Constraints can be either hard constraints which set conditions for thevariables that are required to be satisfied, or soft constraints whichhave some variable values that are penalized in the objective functionif, and based on the extent that, the conditions on the variables arenot satisfied.

According to some embodiments, each constraint may be expressed in termsof a threshold value for a respective quality index of the dosedistribution. The threshold value may be referred to as a “constraintlocation” for the respective quality index. The dose distribution canthen be modified interactively by modifying the constraint locations forthe set of constraints. In this manner, the connection between aclinical goal and a constraint location is maintained. Thus, thephysician's final intent is recorded as the changed constraintlocations.

In some embodiments, a user may assign relative priorities among the setof constraints. According to an embodiment, when a certain constraint ismodified, in the re-optimization, any constraint having a priority thatis higher than that of the modified constraint are forced to be met,while any constraint having a priority that is lower than that of themodified constraint is allowed be violated. In another embodiment, theuser may interactively change the relative priorities for one or moreconstraints. In a further embodiment, two or more constraints may sharethe same priority. In such cases, when a certain constraint is modified,in the re-optimization, other constraints having the same priority areeither forced to be met or are allowed to be violated.

A. Example User Interface for Interactive Dose Manipulation

FIG. 6 illustrates an exemplary user interface that may allow a user tointeractively manipulate the dose distribution of a radiation treatmentplan according to an embodiment of the present invention. The section620 in the middle of the user interface displays DVH curves for variousoptimization structures (e.g., the PTV, an OAR, and the like) thatcorrespond to the initial dose distribution of the initial treatmentplan that was determined using a set of initial set of reference valuesfor a set of quality indexes. The section 630 on the right side of theuser interface displays some two-dimensional slices of thethree-dimensional dose distribution of the initial treatment plan.

The section 610 on the left side of the user interface includes aplurality of fields 611-617. Each field corresponds to a clinical goalin terms of a respective quality index. For instance, in the exampleshown in FIG. 6, the first field 611 corresponds to the maximum doseDmax for the planned target volume (PTV); the second field 612corresponds to the minimum dose Dmin for the PTV; the third field 613corresponds to the mean dose Dmean for an organ at risk (OAR) (e.g., therectum); and the fields 614-617 correspond to various clinical goalsrelating to the dose to an OAR. Each field may include an initialthreshold value for the corresponding treatment goal. For example, inthe field 611, the initial threshold value for Dmax for the PTV isindicated as “Goal: Dmax≤107.00%.”

The display area 618 in the section 610 allows the user to enter newthreshold values (i.e., change the “constraint locations”) for the setof quality indexes. For example, in the field 612, the user may enter95.85% as the new threshold value (i.e., the “desired” value) for Dminto the PTV. The user can edit the number 619 in the display area 618.Alternatively, the user can make a change in the corresponding DVH graphin the middle section 620 of the user interface by dragging a handle 622on the DVH graph to a desired location. For example, the user can dragthe handle 622 of the DVH graph of an OAR to a lower dosage value. Asthe DVH graph is modified, the “desired” threshold value for thecorresponding quality index may be updated accordingly in the displayarea 618.

B. Re-Optimization and Prioritizing Constraints

After the user has changed a threshold value for one of the clinicalgoals as discussed above, the system may re-optimize the treatment planin order to meet the new threshold value for that clinical goal. Sincethe initial treatment plan is typically an optimized solution that isfully determined by multiple constraints, changing a single constraintmay not result in a solution that can also meet all other constraints.In other words, a re-optimized treatment plan may have to violate one ormore other constraints in order to meet the modified constraint.According to an embodiment of the present invention, the set ofconstraints are prioritized. For instance, in the example illustrated inFIG. 6, the constraint Dmax for the PTV is given the highest priority(i.e., having the priority of “1”); the constraint Dmin for the PTV isgiven the second highest priority (i.e., having the priority of “2”);the constraint Dmean for the OAR is given the third highest priority(i.e., having the priority of “3”); and the other constraints are giventhe shared fourth highest priority (i.e., having the priority of “4”).

When a certain constraint is modified, a re-optimized treatment plan isnot allowed to violate any constraint having a priority that is higherthan that of the modified constraint, and is allowed to violate anyconstraint having a priority that is lower than that of the modifiedconstraint. For instance, assume that a user changes the constraintlocation of Dmin for the PTV from 95.00% to 95.85%, as indicated by thecircle 619 in the display area 618. Because the constraint regardingDmax for the PTV has a priority (priority of “1”) that is higher thanthat of the constraint being modified (priority of “2”), a re-optimizedtreatment plan cannot violate the constraint regarding Dmax for the PTV(e.g., the value of Dmax for the PTV cannot be greater than 107.00%). Onthe other hand, because the constraint regarding Dmean for the OAR has apriority (priority of “3”) that is lower than that of the constraintbeing modified, the re-optimized treatment plan may violate theconstraint regarding Dmean for the OAR (e.g., the value of Dmean for theOAR is allowed to go above 40.00 Gy). After re-optimization, the systemmay update the threshold values of lower priority constraints withachievable values. For instance, assuming that the lowest valueachievable for Dmean for the OAR is 42.00 Gy after re-optimization, thesystem may update the threshold value of Dmean for the OAR to 42.00 Gy.

In some embodiments, the user may choose to start with the constraintwith the highest priority, and then proceed to the constraint with thenext highest priority, and so on until all the constraints have beenhandled. In some embodiments, after handling a constraint with a lowerpriority, the user may wish to go back to a constraint with a higherpriority. In this manner, the user can study the trade-offs among thevarious clinical goals until she finds an optimal achievable treatmentplan.

The method of interactive manipulation of the dose distributionaccording to embodiments of the present invention may afford severaladvantages as compared to conventional approaches. For example, in themanner described above, the connection between a clinical goal and aconstraint location is maintained and the physician's intent is recordedas the changed threshold value for the constraint. In contrast, in anapproach where changes are made directly to the dose distribution, onlythe resultant dose distribution is recorded, which may not clearlyconvey the physician's intent, and consequently it may not be clear howthe physician's intent could be transferred to a different fieldarrangement, a different fractionation scheme, or a modified patientanatomy. In addition, in the manner described above, the physician candirectly study the trade-offs among various clinical goals, which maynot be as transparent in an approach where a modified set of clinicalgoals are used to re-optimize the treatment plan.

C. Constraints Having Same Priority and Other Options

In some cases, it may be difficult to determine the relative prioritiesamong two or more clinical goals. Some embodiments can be generalized tocases where more than one clinical goal has the same priority. Forexample, when one constraint is modified, other constraints that havethe same priority as that of the modified constraint, as well as thoseconstraints with higher priorities, are forced to be met in there-optimization; and only those constraints with lower priorities areallowed be violated. In another example, when one constraint ismodified, other constraints that have the same priority as that of themodified constraint, as well as those constraints with lower priorities,are allowed to be violated in the re-optimization. In yet anotherexample, a user may select whether or not other constraints having thesame priority as that of the modified constraint are allowed to beviolated in the re-optimization.

Other user options and user actions may be possible. In one embodiment,the user may select that the constraint with the closest higher priorityis also allowed to be violated in the re-optimization. In anotherembodiment, the user may be allowed to change the relative priorities ofsome of the clinical goals (e.g., as illustrated by the arrow 624 inFIG. 6). In yet another embodiment, instead of assigning priorities tothe clinical goals, the user may select which constraints are allowed tobe violated and which ones are forced to be met, so that she can studytrade-offs among the various clinical goals. In a further embodiment,the user can create a new clinical goal as a new constraint, and thesystem may perform re-optimization including the newly added clinicalgoal.

D. Modification of Optimization Structure

According to another embodiment, to allow a user to alter thethree-dimensional dose distribution directly (so-called “paintingdose”), the user can change the shape of an optimization structure, suchas the contour of a PTV or an OAR. An interactive user action can besimilar to using a brush tool in a painting application where the useris provided a “brush” with which she can change the shape of anoptimization structure (thus this method may be referred to as “paintingstructure”). For example, if the user thinks that radiation dose shouldbe delivered to a larger volume than the current volume of the PTV, theuser can enlarge the contour of the PTV to enlarge its volume. Thesystem may re-optimize the radiation treatment plan according to theenlarged PTV.

FIG. 7 illustrates an exemplary user interface that can allow a user tointeractively manipulate the dose distribution of a radiation treatmentplan by changing the shape of an optimization structure, according to anembodiment of the present invention. The section 710 on the left side ofthe user interface includes a plurality of fields, each fieldcorresponds to a clinical goal with respect to an optimizationstructure. For example, the field 712 corresponds to dose coverage ofthe PTV (i.e., percentage of the PTV receiving 100% of the prescribeddose).

The section 730 on the right side of the user interface displays atwo-dimensional slice of the three-dimensional dose distribution. If theuser thinks that radiation dose should be delivered to a larger volumethan the current volume of the PTV, she may select the field 712 in thesection 710 that corresponds to dose coverage to the PTV. In response tothe selection of field 712, the contour 736 of the PTV would becomeactive in the dose distribution image in the section 730 of the userinterface. For example, the contour 736 of the PTV may be depicted inred color, as illustrated in FIG. 7. The user may then select the brushtool icon 732 on the top of the section 730. The cursor would then bechanged into a “brush” 734. The user can use the brush to make contour736 of the PTV larger by painting it larger. In one embodiment, thesystem may re-optimize the radiation treatment plan according to theenlarged PTV.

E. Alternative Embodiment

According to another embodiment, a method of interactive manipulation ofthe dose distribution of a radiation treatment plan may be described asfollows. First, an initial set of candidate treatment plans aregenerated by selecting all treatment plans that can be realized with theselected patient geometry and field geometry restrictions. Next, a setof clinical goals are converted into a set of constraints. The set ofconstraints are ranked with relative priorities in an order ofimportance.

According to an embodiment, a physician may start with modifying theconstraint having the highest priority, and check if there exists asubset of the candidate treatment plans satisfying the modifiedconstraint that is non-empty. If the subset is non-empty, that clinicalgoal is marked as met and the initial set of candidate treatment plansis replaced by the subset. If the subset is empty (i.e., none of thetreatment plans in the initial set can meet the modified constraint),that clinical goal is marked as not met. In one embodiment, the initialset of candidate treatment plans is kept unchanged. In anotherembodiment, the initial set of candidate treatment plans is replacedwith a subset where the quality index value associated to that clinicalgoal reaches a value that is as close to clinically acceptable value aspossible. In one embodiment, the constraint location for that clinicalgoal may be updated to the location that is achievable. The physicianmay then proceed to handle the constraint of the next highest priority.This process may be repeated until all constraints have been handled.

According to an embodiment, once all clinical goals have been handled, afinal optimal treatment plan may be selected from the final subset oftreatment plans. In some embodiments, the final optimal treatment planmay be obtained by optimizing an appropriate cost function. For example,the cost function may be designed to minimize the amount of violation ofthe most important un-met constraint. Alternatively, the cost functionmay be designed to leave as much margin as possible for the mostimportant fulfilled constraint. Other criteria may also be used in theconstruction of the cost function. The optimized treatment plan may beconsidered as optimally fulfilling the set of clinical goals.

F. Method

FIG. 8 shows a simplified flowchart illustrating a method 800 forinteractively manipulating dose distribution of a radiation treatmentplan using an external-beam radiation treatment system according to anembodiment of the present invention.

At 802, an initial radiation treatment plan is obtained. The initialradiation treatment plan produces an initial dose distribution thatsatisfies a plurality of clinical goals. The plurality of clinical goalsare expressed in terms of a plurality of initial threshold values for aplurality of quality indexes. Each quality index relates to a respectivestatistical quantity of the initial dose distribution.

At 804, the plurality of clinical goals is converted into a plurality ofconstraints relating to the plurality of quality indexes. Eachconstraint has a respective initial reference value corresponding to theinitial threshold value of the respective quality index. In oneembodiment, each respective constraint has a corresponding priorityindicating relative importance of the respective constraint among theplurality of constraints.

At 806, a user interface, such as that illustrated in FIG. 6, isprovided to a user. The user interface allows the user to change aninitial reference value to a new reference value for one of theplurality of constraints. The user can either type in a new numericalvalue in the user interface or drag a handle in a corresponding DVHcurve in the user interface, as discussed above in relation to FIG. 6.

At 808, re-optimization of the initial radiation treatment plan isperformed to obtain an updated radiation treatment plan using the newreference value for the one of the plurality of constraints. In oneembodiment, the updated radiation treatment plan produces an updateddose distribution that satisfies any constraint that has a higherpriority than the one of the plurality of constraints while allowing anyconstraint that has a lower priority than the one of the plurality ofconstraints to be violated.

In some embodiments, the updated radiation treatment plan includes acontrol-point sequence and a multileaf collimator (MLC) leaf sequence tobe used by the external-beam radiation treatment system for deliveringradiation to a patient. The updated radiation treatment plan may betransmitted to control circuitry of the external-beam radiationtreatment system to cause the external-beam radiation treatment systemto deliver the radiation to the patient according to the control-pointsequence and the multileaf collimator (MLC) leaf sequence of the updatedradiation treatment plan.

IV. Radiation Treatment Planning Based on Clinical Goals with SharedPriorities

Optimization is often used in IMRT to achieve a treatment plan that bestfits a set of clinical goals. Since in general it is not guaranteed thatall clinical goals can be fulfilled simultaneously for a particularpatient geometry, it may be necessary to prioritize the clinical goals.One approach may be to search a treatment plan that fulfills as manyhigher priority clinical goals as possible. A prioritized constrainttechnique, such as the technique of lexicographic ordering, may be usedin this approach. The optimization process typically starts with onlythe highest priority clinical goal. Once a solution meeting thatclinical goal is found, the clinical goal is changed to a constraint.Another optimization is then performed using the next highest priorityclinical goal as the new optimization objective. This process may berepeated for the remaining clinical goals. If a particular clinical goalcannot be fulfilled, the constraint is set to a value that isacceptable.

A. Using Shared Priorities in Clinical Goal Setting

In some cases, however, it may be difficult to assign a unique priorityto each of the clinical goals, or there may be two or more clinicalgoals that are considered as equally important and yet cannot both befulfilled at the same time. For instance, consider the exampleillustrated in FIG. 9. The horizontal axis and the vertical axis are thevalues of a first quality index Q₁ and a second quality index Q₂,respectively. For example, the first quality index Q₁ may relate to themean dose Dmean to an OAR (e.g., the spine), and the second qualityindex Q₂ may relate to the maximum dose Dmax to a PTV. A first clinicalgoal may be expressed in terms of the first quality index Q₁ as Q₁≤x₀,represented by the vertical straight line 910; and a second clinicalgoal may be expressed in terms of the second quality index Q₂ as Q₂≤y₀,represented by the horizontal straight line 920. The shaded area 930 inthe lower left quadrant may represent a region where both the firstclinical goal and the second clinical goal are simultaneously satisfied.

In some cases, however, for a particular set of patient geometry andfield geometries, an achievable solution may not be found where both thefirst clinical goal and the second clinical goal can be fulfilled at thesame time. For instance, the shaded region 940 represents the regionwhere achievable solutions can be found for a set of given patientgeometry and field geometries. In this example, there is no overlapbetween the shaded region 940 and the shaded region 930, which meansthat there is no achievable solution that can fulfill both the firstclinical goal and the second clinical goal simultaneously.

In such a case, the point 960, where the vertical line 910 and theborder line 950 of the region 940 intersects, may represent anachievable solution that fulfills the first clinical goal with a minimumamount of violation of the second clinical goal. Similarly, the point970, where the horizontal line 920 and the border line 950 of the region940 intersects, may represent an achievable solution that fulfills thesecond clinical goal with a minimum amount of violation of the firstclinical goal. Thus, if the first clinical goal is considered to be moreimportant than the second clinical goal, then the point 960 mayrepresent an optimal treatment plan. On the other hand, if the secondclinical goal is considered to be more important than the first clinicalgoal, the point 970 may represent an optimal treatment plan. However, incases where it is not clear whether the first clinical goal is moreimportant than the second clinical goal or vice versa, or the firstclinical goal and the second clinical goal are equally important,perhaps neither the point 960 nor the point 970 represents an optimalsolution.

For cases where two or more clinical goals share the same priority or itis not clear which clinical goal is more important than the other,embodiments may be designed to seek a solution that minimizes the“distance” to the region where all the clinical goals are met. Forinstance, in the example illustrated in FIG. 9, a solution representedby the point 980, which is located somewhere between the point 960 andthe point 970 along the border line 950 of the region 940. At the point980, although neither the first clinical goal nor the second clinicalgoal is met, it may have the closest “distance” to the region 930 whereboth the first clinical goal and the second clinical goal are met.

B. Specifying Two Sets of Threshold Values for a Set of Clinical Goals

Referring to FIG. 10, consider two quality indexes Q₁ and Q₂,represented by the horizontal axis and the vertical axis, respectively.According to an embodiment of the present invention, a user may specifya first set of threshold values for Q₁ and Q₂ as follows:

Q ₁ ≤x ₀, and Q ₂ ≤y ₀.

The first set of threshold values (x₀, y₀) may be represented by thepoint 1032 in FIG. 10. In addition, the user may specify a second set ofthreshold values for Q₁ and Q₂ as follows:

Q ₁ ≤x ₁, and Q ₂ ≤y ₁,

where x₁>x₀, and y₁>y₀. The second set of threshold values (x₁, y₁) maybe represented by the point 1042 in FIG. 10. Thus, it may be easier tofulfill to the second set of threshold values (x₁, y₁) than the firstset of threshold values (x₀, y₀), as the second set of threshold valuesare higher. The user may assign a higher priority for meeting the secondset of threshold values, and a lower priority for meeting the first setof threshold values. For example, the second set of threshold values(x₁, y₁) may represent clinically acceptable threshold values for thequality indexes Q₁ and Q₂ and thus has to be met, whereas the first setof threshold values (x₀, y₀) may represent desired or preferredthreshold values for the quality indexes Q₁ and Q₂ and can be violated.In one embodiment, the point 1032 resides outside the region 1040 whereachievable solutions can be found; and the point 1042 resides inside theregion 1040. In other words, the first set of clinical goals (x₀, y₀)cannot be simultaneously fulfilled, while the second set of clinicalgoals (x₁, y₁) can be simultaneously fulfilled.

An optimizer may construct a cost function designed to reach a solutionrepresented by the point 1080, where the straight line connecting thepoint 1032 and the point 1042 intersects with the border line 1050 ofthe region 1040 where solution can be found. The point 1080 mayrepresent an achievable solution that has the minimum “distance” to theregion where the first set of threshold values are simultaneously met.As can be seen in FIG. 10, the location of the point 1080 may depend onthe values of δx and δy, where δx=x₁−x₀, and δy=y₁−y₀. In a case whereδx=0 and δy is finite, the optimal solution may be represented by thepoint 1060 where the clinical goal of x₀ for Q₁ is met. This may be thecase where the threshold value x₀ for Q₁ is so critical such that it hasto be met. Conversely, in a case where δy=0 and δx is finite, theoptimal solution may be represented by the point 1050 where thethreshold value of y₀ for Q₂ is met. This may be the case where thethreshold value y₀ for Q₂ is so critical such that it has to be met.

For cases where both δx and δy are non-zero, a cost function may beconstructed to include a weighted sum of two quadratic terms as:

z=w ₁{max[0,(Q ₁ −x ₀)]}² +w ₂{max[0,(Q ₂ −y ₀)]}²,  (1)

where

${w_{1} = \frac{1}{\left( {\delta \; x} \right)^{2}}},{{{and}\mspace{14mu} w_{2}} = {\frac{1}{\left( {\delta \; y} \right)^{2}}.}}$

Thus, an increase in Q₁ in excess of x₀, as well as an increase in Q₂ inexcess of y₀, will incur increasing cost, and the relative weights ofthe first term and the second term are inversely proportional to squareof δx and δy, respectively. Therefore, if δx>δy, the second term wouldhave a greater weight than the first term; conversely, if δy>δx, thefirst term would have a greater weight than the first term. The costfunction as expressed in Equation (1) may guide the optimizer toward asolution represented by the point 1080 in FIG. 10, which may beconsidered as the optimal solution having a minimum weighted “distance”to the region where the desired threshold values of (x₀, y₀) aresimultaneously fulfilled. In other embodiments, the terms of the costfunction may have forms other than quadratic functions. For example,they may be polynomial functions of an order higher than two, or theymay be exponential functions. In some embodiments, the weights w₁ and w₂may have forms other than quadratic functions as well. For example, theymay be polynomial functions of an order higher than two, or they may beexponential functions. It should be understood that, although the abovediscussion refers to only two clinical goals expressed in terms of twoquality indexes, embodiments can be extended to cases where more thantwo clinical goals expressed in terms of more than two quality indexesare considered.

C. Specifying Threshold Values as Well as Insignificant Changes for aSet of Quality Indexes

In an alternative embodiment, instead of defining a first set ofthreshold values (x₀, y₀) and a second set of threshold values (x₁, y₁),the user may define a set of desired threshold values (x₀, y₀), and aset of clinically insignificant changes for Q₁ and Q₂ as (δx, δy). Acost function similar to the cost function expressed in Equation (1) maybe used to find an optimal solution.

D. Situations where a Set of Clinical Goals can be FulfilledSimultaneously

The optimization method described above can also be applied to caseswhere the desired threshold values (x₀, y₀) can be simultaneouslyfulfilled. For instance, consider the example illustrated in FIG. 11.Here, the point 1132 corresponding to (x₀, y₀) is located within theregion 1140 where solutions can be found. As such, all solutions locatedwithin the portion of the region 1140 that is below the horizontal line1120 and to the left of the vertical line 1110 may satisfy both of thedesired threshold values x₀ and y₀. Therefore, an optimal treatment planmay not be uniquely defined. The solution corresponding to the point1160 may provide the largest margin to the desired threshold value x₀for the quality index Q₁ (i.e., the largest amount by which the actualvalue of the quality index Q₁ falls below the desired threshold valuex₀), whereas the solution corresponding to the point 1170 may providethe largest margin to the desired threshold value y₀ for the qualityindex Q₂.

Instead of seeking a solution that provides the largest margin to thedesired threshold value for either of the quality indexes Q₁ and Q₂, theoptimizer may seek a solution that maximizes the margin in terms of the“distance” to the point 1132 having the desired threshold values (x₀,y₀). Assume that the point 1142 corresponds to the acceptable thresholdvalues (x₁, y₁). In one embodiment, the optimizer may seek to find asolution represented by the point 1180, where the extension of thestraight line connecting the point 1132 and the point 1142 intersectswith the border line 1150 of the region 1140, as point 1180 may providethe largest margin in terms of the weighted “distance” to the point1132.

E. Example User Interface

FIG. 12 illustrates an exemplary user interface that may be used in theoptimization process according to an embodiment of the presentinvention. The section 1210 on the left side of the user interfaceincludes a plurality of fields 1211-1217. Each field corresponds to aclinical goal with regard to a respective quality index. For eachclinical goal, a user may specify a first threshold value and a secondthreshold value for the respective quality index. In some embodiments,the first threshold value may be a preferred value, and the secondthreshold value may be an acceptable value. For instance, in the exampleillustrated in FIG. 12, the first threshold value is shown as the“GOAL,” and the second threshold value is shown as the “Var.” Forexample, in the first field 1211, the first threshold value for Dmax tothe PTV is specified to be 105%, and the second threshold value for Dmaxto the PTV is specified to be 107%. In some embodiments, the user mayinteractively change the first threshold value and/or the secondthreshold value for each clinical goal during the optimization process.The optimizer may perform optimization of a treatment plan based on thespecified threshold values for the clinical goals using the methoddescribed above.

F. Method

FIG. 13 shows a simplified flowchart illustrating a method 1300 ofdetermining an optimal radiation treatment plan using an external-beamradiation treatment system according to an embodiment of the presentinvention.

At 1302, a first clinical goal and a second clinical goal are receivedvia a user interface of a computer system. The first clinical goalincludes a first acceptable threshold value and a first desiredthreshold value for a first quality index. The second clinical goalincludes a second acceptable threshold value and a second desiredthreshold value for a second quality index. In some embodiments, thedifference between the first acceptable threshold value and the firstdesired threshold value may correspond to a clinically insignificantchange for the first quality index, and the difference between thesecond acceptable threshold value and the second desired threshold valuemay correspond to a clinically insignificant change for the secondquality index.

At 1304, a cost function is obtained. The cost function includes a firstterm with a first weight and a second term with a second weight. Thefirst term is proportional to a value of the first quality index inexcess of the first acceptable threshold value, and the second term isproportional to a value of the second quality index in excess of thesecond acceptable threshold value. The first weight is inverselyproportional to a difference between the first desired threshold valueand the first acceptable threshold value, and the second weight isinversely proportional to a difference between the second desiredthreshold value and the second acceptable threshold value.

At 1306, optimization is performed using the cost function to obtain anoptimal radiation treatment plan that has an optimal value for the costfunction.

In some embodiments, the first term of the cost function is proportionalto square of the value of the first quality index in excess of the firstacceptable threshold value, and the second term is proportional tosquare of the value of the second quality index in excess of the secondacceptable threshold value. The first weight is inversely proportionalto square of the difference between the first desired threshold valueand the first acceptable threshold value, and the second weight isinversely proportional to square of the difference between the seconddesired threshold value and the second acceptable threshold value. Forexample, the cost function may have the form expressed in Equation (1).

V. Generating a Radiation Treatment Plan Based on Clinical Goals andTrade-Offs Among the Clinical Goals

In optimizing a radiation treatment plan, it is often necessary tointerpret a set of user defined clinical goals in terms of a costfunction. The cost function assigns a single scalar value for each planas a function of all the “microscopic” degrees of freedom (MDF) in thetreatment plan. The MDF can be the set of all fluence pixels in allfields or the set of all free machine parameters needed to deliver thetreatment plan. The optimization problem may be then reduced to findinga plan that has the minimum cost function value.

In some cases where more than one clinical goals are provided, it maynot be guaranteed that all clinical goals can be fulfilledsimultaneously, as described in the previous section in relation to FIG.9. One approach may be to also specify the relative priorities of thedifferent clinical goals, so as to instruct the optimizer which goalshould be fulfilled first. On the other hand, in some cases there may bemore than one treatment plans that can satisfy all clinical goals. Forinstance, in the example illustrated in FIG. 11, any point in theportion of region 1140 below the horizontal straight line 1120 and tothe left of the vertical straight line 1110 may represent a solutionthat satisfies both clinical goals (x₀, y₀) simultaneously. In suchcases, the set of clinical goals (x₀, y₀) may not uniquely determine anoptimal plan, but only reduces the set of achievable plans.

A. Cost Function Based on Clinical Goals

Consider a case where two clinical goals are presented in terms ofthreshold values for two quality indexes Q₁ and Q₂ as Q₁≤x₀ and Q₂≤y₀.One way of constructing a cost function is to include a weighted sum oftwo quadratic terms as,

z=w ₁{max[0,(Q ₁ −x ₀)]}² +w ₂{max[0,(Q ₂ −y ₀)]}²,  (2)

where w₁ and w₂ are the weights for the two quadratic terms. Referringto FIG. 14, the point 1410 correspond to the threshold values (x₀, y₀)and may be referred to as the “objective location.” The contour lines1420 a-1420 e represent a set of iso-curves of the cost function z. Theobjective of an optimization may be to minimize the value of the costfunction z for a set of patient geometry and field geometries. Forinstance, in the example illustrated in FIG. 14, the shaded region 1440represents the region where achievable solutions can be found for agiven patient geometry. The point 1442 where the iso-curve 1420 e justtouches the border line 1450 of the region 1440 may represent an optimalachievable solution that has the lowest possible cost function value.

The constraint location 1410 is usually chosen such that the referencevalues (x₀, y₀) are related to but not the same as clinically acceptablethreshold values for Q₁ and Q₂. In other words, the objective location1410 is usually selected to be outside the region 1440, so that the costfunction has a finite gradient and thus can be minimized. Choosing theobjective location 1410 usually requires some experience. According tosome embodiments, users may set the objective location manually.

B. Trade-Offs Between Clinical Goals

In some cases, however, it may be problematic to use a static costfunction that only depends on the threshold values for the clinicalgoals. In some cases, a physician may not consider a treatment plan thatsatisfies a set of clinical goals as the best possible plan. Forinstance, consider the examples illustrated in FIG. 15. The point 1510is the objective location. Contour lines 1520 a-1520 g are theiso-curves of a cost function as expressed in Equation (2). Consider afirst case where a first feasible solution space for a first patientgeometry is defined by the first border curve 1550. In this case, thepoint 1552, where the iso-curve 1520 g of the cost function just touchesthe first border curve 1550, may represent a potential optimal solution.Now consider a second case where a second feasible solution space for asecond patient geometry is defined by the second border curve 1560.Here, the point 1562, where the iso-curve 1520 g of the cost functionjust touches the second border curve 1560, may represent a potentialoptimal solution. Thus, although the solution corresponding to the point1552 and the solution corresponding to the point 1562 lie on the sameiso-curve and hence have the same cost function value, the two solutionsare obviously very different. This illustrates that the same form ofcost function may lead to very different solutions depending on theshape of the solution space.

In some cases, a physician may prefer to consider trade-offs between twoquality indexes where much can be gained in one quality index withoutreducing significantly the other. For instance, in the first exampleillustrated in FIG. 15, the point 1552 lies on a section of the firstborder curve 1550 where it is substantially horizontal. This means thatanother solution in the vicinity of the point 1552 along the bordercurve 1550 may only incur a small change in the value of Q₂ but can havea large reduction in the value of Q₁. For example, consider thealternative solution represented by the point 1554. Its value of Q₂ isonly slightly increased from the value of Q₂ at the point 1552, yet itsvalue of Q₁ is significantly reduced from the value of Q₁ at the point1552. Thus, a physician may prefer the alternative solution representedby the point 1554 over the solution represented by the point 1552, aslong as the increase in the value of Q₂ is within the clinicallyinsignificant change of Q₂.

Similarly, in the second example illustrated in FIG. 15, the point 1562lies on a section of the second border curve 1560 where it issubstantially vertical. This means that another solution in the vicinityof the point 1562 along the border curve 1560 may only incur a smallchange in the value of Q₁ but can have a large reduction in the value ofQ₂. For example, consider the alternative solution represented by thepoint 1564. Its value of Q₁ is only slightly increased from the value ofQ₁ at the point 1562, yet its value of Q₂ is significantly reduced fromthe value of Q₂ at the point 1562. Thus, a physician may prefer thealternative solution represented by the point 1564 over the solutionrepresented by the point 1562, as long as the increase in the value ofQ₁ is within the clinically insignificant change of Q₁. In cases wherethe objective location is far inside the region where the solution canbe found, consideration of trade-offs may be even more important, asoptimization may be driven by some secondary terms, such as fluencesmoothing and monitor unit (MU) count objectives.

C. Cost Function Based on Clinical Goals and Trade-Offs Among ClinicalGoals

As discussed above with relation to FIG. 15, it may be desirable toconstruct a cost function that not only takes into account a set ofclinical goals, but also possible trade-offs among the set of clinicalgoals. According to embodiments of the present invention, an optimizercan support clinical goals where the user has specified preferabletrade-offs in advance. For example, the user can specify clinicallyinsignificant changes as well as clinically significant changes for eachquality indexes. In some embodiments, the cost function can be generatedand dynamically altered during optimization so that any solutionachieving clinically significant improvement in one quality index whileonly deteriorating the other quality index by an insignificant amountmay be accepted. In one embodiment, the optimizer may change theobjective location whenever the cost function gradient in a spacespanned by the quality indexes has a much greater component with respectto one quality index compared to the other quality index.

According to an embodiment of the present invention, a cost function mayinclude a term relating to threshold values for the quality indexes, aswell as terms relating to user-specified clinically insignificant andclinically significant changes for the quality indexes. For example,consider two clinical goals involving a first quality index Q₁ and asecond quality index Q₂. The optimizer may construct a cost function zthat may include the following three terms,

$\begin{matrix}{\sqrt{\left. {{w_{1}^{2}\left\{ {\max \left\lbrack {0,\left( {Q_{1} - x_{0}} \right)} \right\rbrack} \right\}^{2}} + {w_{2}^{2}\left\{ {\max \left\lbrack {0,\left( {Q_{2} - y_{0}} \right)} \right\rbrack} \right\}^{2}}} \right\}},} & (3) \\{{{w_{1}\delta \; {x_{L} \cdot Q_{1}}} + {w_{2}\delta \; {y_{H} \cdot Q_{2}}} + {ax}},} & (4) \\{{{w_{1}\delta \; {x_{H} \cdot Q_{1}}} + {w_{2}\delta \; {y_{L} \cdot Q_{2}}} + {bx}},} & (5)\end{matrix}$

where each term presents the cost function in a different region of the(Q₁, Q₂) plane. The values of x₀ and y₀ define a constraint location;δx_(L), and δy_(L) are the user-specified clinically insignificantchanges in Q₁ and Q₂, respectively; δx_(H) and dy_(H) are theuser-specified clinically significant changes in Q₁ and Q₂,respectively; w₁ and w₂ are relative weights. The region borders and theparameters a and b are selected so that the cost function contours arecontinuous and smooth. Normally δx_(H)>δx_(L), and dy_(H)>δy_(L). Forexample, assume that Q₁ corresponds to the maximum dose Dmax to an OAR.A user may specify that the clinically insignificant change for Q₁δx_(L) is 0.5 Gy, and the clinically significant change for Q₁ δx_(H) is5 Gy.

In some embodiments, the second term expressed in Equation (4) and thethird term expressed in Equation (5) may guide the optimization toward asolution that keeps the quality index gradients within the bounds ofδx_(L) and δy_(L), and δx_(H) and dy_(H). For example, referring to FIG.15, in the case where the border line for the region where the solutioncan be found is defined by the curve 1550, the new cost function may bedesigned to have its iso-curves shaped such that it may lead to thesolution located at point 1554 instead of 1552, so as to take advantageof the beneficial trade-offs. On the other hand, in the case where theborder line for the region where the solution can be found is defined bythe curve 1560, the new cost function may be designed to have itsiso-curves shaped such that it will lead to the solution located atpoint 1564 instead of 1562, so as to take advantage of the beneficialtrade-offs. It should be understood that, although the above discussionrefers to only two quality indexes, the method can be extended to caseswhere more than two quality indexes are considered.

In some embodiments, instead of specifying clinically significantchanges and clinically insignificant changes for the quality indexes,the user may specify desired threshold values as well as acceptablethreshold values for the quality indexes. For example, the user mayspecify the desired threshold values for Q₁ and Q₂ as x₀ and y₀,respectively, and specify the acceptable threshold values for Q₁ and Q₂as x₁ and y₁, respectively, where x₁>x₀ and y₁>y₀. The desired thresholdvalues x₀ and y₀ would be the primary driver for the optimization, andthe acceptable threshold values x₁ and y₁ are used to constrain theoptimizer's search for user preferred trade-offs.

D. Cost Function Including Cross Terms Among Clinical Goals

In another embodiment, the optimizer may construct a cost function zthat includes the following two terms,

w ₁{max[0,(Q ₁ −x ₀)]}² +w ₂{max[0,(Q ₂ −y ₀)]}²,  (6)

w ₁₂ max{0,(Q ₁ −x ₀)}max{0,(Q ₂ −y ₀)},  (7)

where the weights w₁, w₂, and w₁₂ are selected such that certain qualityindex gradients are preferred. The cross term expressed in Equation (7)may guide the optimizer toward an optimal solution that takes advantagesof any beneficial trade-offs.

E. Dynamic Change of Objective Location

According to an embodiment of the present invention, the optimizer maychange the objective location whenever the cost function gradient in aspace spanned by the quality indexes has a much greater component withrespect to one quality index compared to the other quality index. Forinstance, in the example illustrated in FIG. 15, consider the solutioncorresponding to the point 1552. Since this point is almost directlyabove the constraint location 1510, the cost function value at thispoint has a much greater contribution from the term w₂ {max [0,(Q₂−y₀)]}² than from the term w₁ {max [0, (Q₁−x₀)]}². This means thatthe solution 1552 is located at a position where the gradient of thequality index Q₁ is very high, i.e., a small reduction in the value ofQ₂ can cause large increase in the value of Q₁. In one embodiment, uponrecognizing such a situation, the optimizer may move the objectivelocation 1510 toward the left, i.e., reducing the value of x₀, so thatthe cost function value may have a greater contribution from the termw₁{max [0, (Q₁−x₀)]}².

F. Other Embodiments

In some embodiments of the present invention, trade-off information maybe deduced from knowledge models. For example, potentially beneficialtrade-offs may be deduced automatically from a selected set of existingtreatment plans using machine learning algorithms, such as those similarto some current DVH estimation algorithms.

In some other embodiments, similar approaches can be used to restrictthe solution space in multi-criteria-optimization (MCO), where the costfunction is a vector valued function.

The optimization approaches described above may afford severaladvantages. For example, in cases where a set of clinical goals does notuniquely determine an optimal plan but only reduces the set ofachievable plans, or in cases where not all clinical goals can besatisfied, taking into account information about the acceptable orpreferred trade-offs in the optimization can guide the optimizer to theoptimal treatment plan.

G. Example User Interface

FIG. 16 illustrates an exemplary user interface that may be used in theoptimization process according to an embodiment of the presentinvention. The section 1610 on the left side of the user interfaceincludes a plurality of fields 1611-1617. Each field corresponds to aclinical goal with regard to a respective quality index. In someembodiments, for each clinical goal, a user may specify a desiredthreshold value (i.e., the “GOAL”), as well as a clinically “significantchange” and a clinically “insignificant change,” for the respectivequality index. For example, in the first field 1611, the desiredthreshold value for Dmax to the PTV is specified to be 105%, theclinically significant change is specified to be 1%, and the clinicallyinsignificant change is specified to be 0.1%. The system may optimize atreatment plan based on the user-specified threshold values, as well asclinically significant changes and clinically insignificant changes. Insome embodiments, the user may interactively change the desiredthreshold values, as well as the clinically significant changes and theclinically insignificant changes during the optimization process.

H. Method

FIG. 17 shows a simplified flowchart illustrating a method 1700 ofdetermining an optimal radiation treatment plan using an external-beamradiation treatment system according to an embodiment of the presentinvention.

At 1702, a first clinical goal and a second clinical goal is receivedvia a user interface of a computer system. The first clinical goalincludes a first threshold value for a first quality index relating to afirst statistical quantity of a dose distribution. the second clinicalgoal includes a second threshold value for a second quality indexrelating to a second statistical quantity of the dose distribution.

At 1704, a first clinically significant change and a first clinicallyinsignificant change for the first quality index are received. Also, asecond clinically significant change and a second clinicallyinsignificant change for the second quality index are received.

At 1706, a cost function is obtained. The cost function includes a firstterm, a second term, and a third term. The first term is proportional toa value of the first quality index in excess of the first thresholdvalue and proportional to a value of the second quality index in excessof the second threshold value. The second term relates to the firstclinically insignificant change for the first quality index and to thesecond clinically significant change for the second quality index. Thethird term relates to the first clinically significant change for thefirst quality index and to the second clinically insignificant changefor the second quality index. In one embodiment, the first term of thecost function may have the form expressed in Equation (3).

At 1708, optimization is performed using the cost function to obtain anoptimal radiation treatment plan that has an optimal value for the costfunction.

In some embodiments, the second term of the cost function isproportional to a product of the first clinically insignificant changeand the value of the first quality index, and proportional to a productof the second clinically significant change and the value of the secondquality index. For example, the second term may have the form expressesin Equation (4). The third term of the cost function is proportional toa product of the first clinically significant change and the value ofthe first quality index, and proportional to a product of the secondclinically insignificant change and the value of the second qualityindex. For example, the third term may have the form expressed inEquation (5).

VI. Computer System

Any of the computer systems mentioned herein may utilize any suitablenumber of subsystems. Examples of such subsystems are shown in FIG. 18in computer system 1800. In some embodiments, a computer system includesa single computer apparatus, where the subsystems can be the componentsof the computer apparatus. In other embodiments, a computer system caninclude multiple computer apparatuses, each being a subsystem, withinternal components.

The subsystems shown in FIG. 18 are interconnected via a system bus1875.

Additional subsystems such as a printer 1874, keyboard 1878, storagedevice(s) 1879, monitor 1876, which is coupled to display adapter 1882,and others are shown. Peripherals and input/output (I/O) devices, whichcouple to I/O controller 1871, can be connected to the computer systemby any number of means known in the art, such as serial port 1877. Forexample, serial port 1877 or external interface 1881 (e.g. Ethernet,Wi-Fi, etc.) can be used to connect computer system 1800 to a wide areanetwork such as the Internet, a mouse input device, or a scanner. Theinterconnection via system bus 1875 allows the central processor 1873 tocommunicate with each subsystem and to control the execution ofinstructions from system memory 1872 or the storage device(s) 1879(e.g., a fixed disk, such as a hard drive or optical disk), as well asthe exchange of information between subsystems. The system memory 1872and/or the storage device(s) 1879 may embody a computer readable medium.Any of the data mentioned herein can be output from one component toanother component and can be output to the user.

A computer system can include a plurality of the same components orsubsystems, e.g., connected together by external interface 1881 or by aninternal interface. In some embodiments, computer systems, subsystem, orapparatuses can communicate over a network. In such instances, onecomputer can be considered a client and another computer a server, whereeach can be part of a same computer system. A client and a server caneach include multiple systems, subsystems, or components.

It should be understood that any of the embodiments of the presentinvention can be implemented in the form of control logic using hardware(e.g. an application specific integrated circuit or field programmablegate array) and/or using computer software with a generally programmableprocessor in a modular or integrated manner. As used herein, a processorincludes a multi-core processor on a same integrated chip, or multipleprocessing units on a single circuit board or networked. Based on thedisclosure and teachings provided herein, a person of ordinary skill inthe art will know and appreciate other ways and/or methods to implementembodiments of the present invention using hardware and a combination ofhardware and software.

Any of the software components or functions described in thisapplication may be implemented as software code to be executed by aprocessor using any suitable computer language such as, for example,Java, C++ or Perl using, for example, conventional or object-orientedtechniques. The software code may be stored as a series of instructionsor commands on a computer readable medium for storage and/ortransmission, suitable media include random access memory (RAM), a readonly memory (ROM), a magnetic medium such as a hard-drive or a floppydisk, or an optical medium such as a compact disk (CD) or DVD (digitalversatile disk), flash memory, and the like. The computer readablemedium may be any combination of such storage or transmission devices.

Such programs may also be encoded and transmitted using carrier signalsadapted for transmission via wired, optical, and/or wireless networksconforming to a variety of protocols, including the Internet. As such, acomputer readable medium according to an embodiment of the presentinvention may be created using a data signal encoded with such programs.Computer readable media encoded with the program code may be packagedwith a compatible device or provided separately from other devices(e.g., via Internet download). Any such computer readable medium mayreside on or within a single computer product (e.g. a hard drive, a CD,or an entire computer system), and may be present on or within differentcomputer products within a system or network. A computer system mayinclude a monitor, printer, or other suitable display for providing anyof the results mentioned herein to a user.

Any of the methods described herein may be totally or partiallyperformed with a computer system including one or more processors, whichcan be configured to perform the steps. Thus, embodiments can bedirected to computer systems configured to perform the steps of any ofthe methods described herein, potentially with different componentsperforming a respective steps or a respective group of steps. Althoughpresented as numbered steps, steps of methods herein can be performed ata same time or in a different order. Additionally, portions of thesesteps may be used with portions of other steps from other methods. Also,all or portions of a step may be optional. Additionally, any of thesteps of any of the methods can be performed with modules, circuits, orother means for performing these steps.

The specific details of particular embodiments may be combined in anysuitable manner without departing from the spirit and scope ofembodiments of the invention. However, other embodiments of theinvention may be directed to specific embodiments relating to eachindividual aspect, or specific combinations of these individual aspects.

The above description of exemplary embodiments of the invention has beenpresented for the purposes of illustration and description. It is notintended to be exhaustive or to limit the invention to the precise formdescribed, and many modifications and variations are possible in lightof the teaching above. The embodiments were chosen and described inorder to best explain the principles of the invention and its practicalapplications to thereby enable others skilled in the art to best utilizethe invention in various embodiments and with various modifications asare suited to the particular use contemplated.

A recitation of “a”, “an” or “the” is intended to mean “one or more”unless specifically indicated to the contrary.

All patents, patent applications, publications, and descriptionsmentioned here are incorporated by reference in their entirety for allpurposes. None is admitted to be prior art.

What is claimed is:
 1. A computer product comprising a non-transitorycomputer readable medium storing a plurality of instructions that whenexecuted control a computer system to allow interactive manipulation ofdose distribution of a radiation treatment plan using an external-beamradiation treatment system, the instructions comprising: obtaining, bythe computer system, an initial radiation treatment plan, the initialradiation treatment plan producing an initial dose distribution thatsatisfies a plurality of clinical goals, wherein the plurality ofclinical goals are expressed in terms of a plurality of initialthreshold values for a plurality of quality indexes, each respectivequality index relating to a respective statistical quantity of theinitial dose distribution; converting, by the computer system, theplurality of clinical goals into a plurality of constraints relating tothe plurality of quality indexes, each constraint having a respectiveinitial reference value corresponding to the initial threshold value ofthe respective quality index, each respective constraint having acorresponding priority indicating relative importance of the respectiveconstraint among the plurality of constraints; providing a userinterface to a user, the user interface allowing the user to change aninitial reference value to a new reference value for one of theplurality of constraints; and performing, by the computer system,re-optimization of the initial radiation treatment plan to obtain anupdated radiation treatment plan using the new reference value for theone of the plurality of constraints, the updated radiation treatmentplan producing an updated dose distribution, wherein the re-optimizationenforces the updated dose distribution to satisfy any constraint thathas a priority higher than a priority of the one of the plurality ofconstraints while allowing any constraint that has a priority lower thanthe priority of the one of the plurality of constraints to be violated.2. The computer product of claim 1, wherein the updated radiationtreatment plan includes a control-point sequence and a multileafcollimator (MLC) leaf sequence to be used by the external-beam radiationtreatment system for delivering radiation to a patient.
 3. The computerproduct of claim 2, wherein the instructions further comprise:transmitting the updated radiation treatment plan to control circuitryof the external-beam radiation treatment system to cause theexternal-beam radiation treatment system to deliver the radiation to thepatient according to the control-point sequence and the multileafcollimator (MLC) leaf sequence of the updated radiation treatment plan.4. The computer product of claim 1, wherein the updated dosedistribution satisfies the one of the plurality of constraints havingthe new reference value.
 5. The computer product of claim 1, wherein theupdated dose distribution minimizes an amount of violation of eachconstraint that is violated.
 6. The computer product of claim 5, whereinthe updated dose distribution corresponds to an achieved reference valuefor each constraint that is violated, and the instructions furthercomprise replacing the initial reference value of each constraint thatis violated with the achieved reference value.
 7. The computer productof claim 1, wherein another one of the plurality of constraints has asame priority as the one of the plurality of constraints, and whereinthe updated dose distribution satisfies the another one of the pluralityof constraints.
 8. The computer product of claim 1, wherein another oneof the plurality of constraints has a same priority as the one of theplurality of constraints, and wherein the updated dose distribution isallowed to violate the another one of the plurality of constraints. 9.The computer product of claim 1, wherein the instructions furthercomprise: allowing the user to, at the user interface, create a newconstraint corresponding to a new quality index; and performing, by thecomputer system, re-optimization of the updated radiation treatment planto obtain a second updated radiation treatment plan using the newconstraint.
 10. The computer product of claim 1, wherein theinstructions further comprise: allowing the user to, at the userinterface, change priorities of one or more of the plurality ofconstraints; and performing, by the computer system, re-optimization ofthe updated radiation treatment plan to obtain a second updatedradiation treatment plan, the second updated radiation treatment planproduces a second updated dose distribution that satisfies as manyconstraints of higher priorities as possible.
 11. A computer productcomprising a non-transitory computer readable medium storing a pluralityof instructions that when executed control a computer system todetermine a radiation treatment plan for delivering radiation to apatient using an external-beam radiation treatment system, theinstructions comprising: receiving, via a user interface of the computersystem, a first clinical goal and a second clinical goal, wherein thefirst clinical goal includes a first acceptable threshold value and afirst desired threshold value for a first quality index relating to afirst statistical quantity of a dose distribution, and the secondclinical goal includes a second acceptable threshold value and a seconddesired threshold value for a second quality index relating to a secondstatistical quantity of the dose distribution; obtaining, by thecomputer system, a cost function including a first term with a firstweight and a second term with a second weight, wherein the first term isproportional to a value of the first quality index in excess of thefirst acceptable threshold value, and the second term is proportional toa value of the second quality index in excess of the second acceptablethreshold value, and wherein the first weight is inversely proportionalto a difference between the first desired threshold value and the firstacceptable threshold value, and the second weight is inverselyproportional to a difference between the second desired threshold valueand the second acceptable threshold value; and performing, by thecomputer system, optimization using the cost function to obtain anoptimal radiation treatment plan having an optimal value for the costfunction.
 12. The computer product of claim 11, wherein the optimalradiation treatment plan includes a control-point sequence and amultileaf collimator (MLC) leaf sequence to be used by the external-beamradiation treatment system for delivering radiation to a patient. 13.The computer product of claim 12, wherein the instructions furthercomprise: transmitting the optimal radiation treatment plan to controlcircuitry of the external-beam radiation treatment system to cause theexternal-beam radiation treatment system to deliver the radiation to thepatient according to the control-point sequence and the multileafcollimator (MLC) leaf sequence of the optimal radiation treatment plan.14. The computer product of claim 11, wherein the first term of the costfunction is proportional to square of the value of the first qualityindex in excess of the first acceptable threshold value, and the secondterm is proportional to square of the value of the second quality indexin excess of the second acceptable threshold value.
 15. The computerproduct of claim 14, wherein the first weight is inversely proportionalto square of the difference between the first desired threshold valueand the first acceptable threshold value, and the second weight isinversely proportional to square of the difference between the seconddesired threshold value and the second acceptable threshold value. 16.The computer product of claim 11, wherein the difference between thefirst desired threshold value and the first acceptable threshold valueis a clinically insignificant change for the first quality index, andthe difference between the second desired threshold value and the secondacceptable threshold value is a clinically insignificant change for thesecond quality index.
 17. A computer product comprising a non-transitorycomputer readable medium storing a plurality of instructions that whenexecuted control a computer system to determine a radiation treatmentplan for delivering radiation to a patient using an external-beamradiation treatment system, the instructions comprising: receiving, viaa user interface of the computer system, a first clinical goal and asecond clinical goal, wherein the first clinical goal includes a firstthreshold value for a first quality index relating to a firststatistical quantity of a dose distribution, and the second clinicalgoal includes a second threshold value for a second quality indexrelating to a second statistical quantity of the dose distribution;receiving, by the computer system, a first clinically significant changeand a first clinically insignificant change for the first quality index,and a second clinically significant change and a second clinicallyinsignificant change for the second quality index; obtaining, by thecomputer system, a cost function including a first term, a second term,and a third term, wherein the first term is proportional to a value ofthe first quality index in excess of the first threshold value andproportional to a value of the second quality index in excess of thesecond threshold value, the second term relates to the first clinicallyinsignificant change for the first quality index and to the secondclinically significant change for the second quality index, and thethird term relates to the first clinically significant change for thefirst quality index and to the second clinically insignificant changefor the second quality index; and performing, by the computer system,optimization using the cost function to obtain an optimal radiationtreatment plan having an optimal value for the cost function.
 18. Thecomputer product of claim 17, wherein the optimal radiation treatmentplan includes a control-point sequence and a multileaf collimator (MLC)leaf sequence to be used by the external-beam radiation treatment systemfor delivering radiation to a patient.
 19. The computer product of claim17, wherein: the second term of the cost function is proportional to aproduct of the first clinically insignificant change and the value ofthe first quality index, and proportional to a product of the secondclinically significant change and the value of the second quality index;and the third term of the cost function is proportional to a product ofthe first clinically significant change and the value of the firstquality index, and proportional to a product of the second clinicallyinsignificant change and the value of the second quality index.
 20. Thecomputer product of claim 17, wherein the first clinically significantchange and the first clinically insignificant change for the firstquality index, and the second clinically significant change and thesecond clinically insignificant change for the second quality index aredetermined based on a selected set of existing radiation treatmentplans.